;;; *EXAMPLES* ('((string-grobner                                    [VARIABLE]
;;;             (string-grobner "[x^2+y,x-y]" '(x y))
;;;             (string-grobner "[y-x^2,z-x^3]" '(x y z) :order
;;;             #'grevlex>))
;;;             (string-grobner-system
;;;             (string-grobner-system "[u*x+y,x+y]" '(x y) '(u))
;;;             (string-grobner-system "[u*x+y,x+y]" '(x y) '(u)
;;;             :cover '(("[u-1]" "[]")))) (string-read-poly
;;;             (string-read-poly "[x^3+3*x^2+3*x+1]" '(x)))
;;;             (string-elimination-ideal
;;;             (string-elimination-ideal "[x^2+y^2-2,x*y-1]" '(x y)
;;;             1))
;;;             (string-ideal-saturation-1
;;;             (string-ideal-saturation-1 "[x^2*y,y^3]" "x" '
;;;             (x y))) (string-ideal-polysaturation-1
;;;             (string-ideal-polysaturation-1 "[x^2*y,y^3]" "[x,y]"
;;;             '(x y))) (string-cond (string-cond '
;;;             ("[u^2-v]" "[v-1]") '(u v) #'grevlex>))
;;;             (string-cover (string-cover '(("[u^2-v]" "[u]")
;;;             ("[u+v]" "[]")) '(u v) #'grevlex>))
;;;             (string-determine
;;;             (string-determine "[u*x+y,v*x^2+y^2]" '(x y) '(u v)
;;;             :cond '("[u,v]" "[v-1]") :main-order #'lex>))
;;;             (parse-string-to-sorted-alist
;;;             (parse-string-to-sorted-alist "x^2+y^3" '(x y)
;;;             #'grevlex>)
;;;             (parse-string-to-sorted-alist "[x^2+y^3,x-y]" '(x y)
;;;             #'grevlex>))
;;;             (translate-statements
;;;             (translate-statements (collinear a b c)
;;;             (perpendicular a b a c))) (translate-theorem
;;;             (translate-theorem ((perpendicular a b c d)
;;;             (perpendicular c d e f)) ((parallel a b e f)
;;;             (identical-points c d))) (translate-theorem
;;;             ((perpendicular a b a c) (midpoint b c m)
;;;             (midpoint a m o) (collinear b h c)
;;;             (perpendicular a h b c)) ((equidistant m o h o)
;;;             (identical-points b c)))) (prove-theorem
;;;             (prove-theorem ((perpendicular a b c d)
;;;             (perpendicular c d e f)) ((parallel a b e f)
;;;             (identical-points c d))) (prove-theorem
;;;             ((perpendicular a b a c) (midpoint b c m)
;;;             (midpoint a m o) (collinear b h c)
;;;             (perpendicular a h b c)) ((equidistant m o h o)
;;;             (identical-points b c))) (prove-theorem
;;;             ((perpendicular a b a c) (identical-points b c))
;;;             ((identical-points a b) (identical-points a c)))
;;;             (prove-theorem ((perpendicular a b a c)
;;;             (identical-points b c)) ((identical-points a b)
;;;             (real-identical-points a c))))))
;;;    A list of available examples.
;;;
;;; EXAMPLE (symbol &optional (stream t))                            [FUNCTION]
;;;    Run short examples associated with a symbol, which typically is a
;;;    function name. 
;;;
;;; RUN-EXAMPLE (e stream)                                           [FUNCTION]
;;;    Evaluate a single form E and send output to stream STREAM.
;;;
;;; ALL-EXAMPLES (&optional (stream t))                              [FUNCTION]
;;;    Run all available examples and send output to STREAM.
;;;